INTRODUCTION S. CERVENY, 1 A. J. MARZOCCA 1,2. Pabellón 1, Buenos Aires 1428, Argentina. Received 5 July 1998; accepted 4 December 1998

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1 Analysis of Variation of Molecular Parameters of Natural Rubber during Vulcanization in Conformational Tube Model. II. Influence of Sulfur/Accelerator Ratio S. CERVENY, 1 A. J. MARZOCCA 1,2 1 Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento Física, LPMPyMC, Pabellón 1, Buenos Aires 1428, Argentina 2 FATE SAICI, Avenue Blanco Encalada 3003, San Fernando, Prov. Buenos Aires 1644, Argentina Received 5 July 1998; accepted 4 December 1998 ABSTRACT: A natural rubber (NR) with a conventional sulfur cure system and a ratio of sulfur/accelerator ( ) equal to 3 was investigated. The network structure of the NR during vulcanization was analyzed using a model of rubber elasticity based on the tube concept, which was applied to the treatment of the stress strain measurements. The influence of cure time and temperature on the chemical crosslinks density was analyzed. The values were compared with those obtained by means of an equilibrium volume swelling measurement. The differences between samples of NR cured with 3 and 1.5 were analyzed John Wiley & Sons, Inc. J Appl Polym Sci 74: , 1999 Key words: tube model; crosslink density; swelling; natural rubber vulcanizates INTRODUCTION The studies of systems of vulcanization of elastomers by sulfur dominate various investigations. 1 3 It is known that the rubbers are vulcanized at different conditions and with diverse chemicals to achieve an optimum balance of their mechanical properties. Although vulcanization takes place by heat and pressure in the presence of sulfur, the process is relatively slow. A faster process can be achieved by adding small amounts of chemicals known as accelerators. The quantity and kind of crosslinks formed during vulcanization are determined by the relative amounts of accelerator and sulfur used in the cure. Crosslink density is an important factor that affects the physical properties of the vulcanized Correspondence to: S. Cerveny (scerveny@df.uba.ar). Contract grant sponsor: University of Buenos Aires, Argentina; contract grant number: EX205. Journal of Applied Polymer Science, Vol. 74, (1999) 1999 John Wiley & Sons, Inc. CCC /99/ elastomer network. The crosslink density of a compound depends mainly on the polymer, composition and accelerator type, time and temperature of cure, and the accelerator/sulfur ratio. 3,4 There are several methods to estimate the crosslink density. Swelling by an organic solvent is one of the methods for characterizing elastomeric networks. 5 8 This process gives quantitative information about the crosslink density and its composition (mono-, di-, and polysulfide crosslinks). Stress strain measurement is another indirect method for determining the crosslink density. 9,10 The analysis of uniaxial stress strain data of unfilled and filled polymer networks in the frame of the conformational tube model allows a proper separation of the crosslink and constraint contributions to the mechanical behavior and gives a reliable determination of the crosslink densities This work deals with the structures of natural rubber (NR) vulcanizates with an accelerator/sulfur ratio of 3 in its composition at different cure levels achieved at two different tempera- 2747

2 2748 CERVENY AND MARZOCCA tures and times of cure. The chemical crosslinks in the network are determined by means of stress strain and equilibrium volume swelling measurements. The sstress strain data are analyzed using the tube approach developed by Heinrich et al. 9 Also, the change in the molecular parameters of the model with the degree of cure are obtained. Swelling measurements are performed and these results are used to determine the density of active crosslinks. These results are compared with those reported in a previous article 11 on NR vulcanized at different conditions of cure and a conventional cure system in which the ratio of the sulfur/accelerator was 1.5. THEORETICAL The tube model for crosslink networks assumes that, because of the topological constraints, the motion of the chain is essentially confined in a tubelike region made of the surrounding polymers. Heinrich et al. 9,10 presented a relationship between stress,, and strain,, based on a tube model considering moderately crosslinked rubbers. In this model, the reduced stress is expressed as with M 2 G c G n f (1) f (2) where M is the Mooney stress; is the expansion ratio (1 ); describes the relaxation of the deformed tube in the deformed state to an undeformed tube corresponding to the equilibrium state 10 ; and G c and G n represent the crosslink and the constraint contributions of the modulus, respectively. They are connected to the molecular parameters by 10 G c AkT v c G n kt n st l 2 st d o 2 N A 2 M n (3) (4) with d o n l st l 3 st 1/2 (5) st where n st is the segment number density, l st is the length of the statistical segment, d o is the fluctuation range of a chain segment; c is the network chain density; M n,, and are the number average molecular weight of the primary chains, the polymer density, and the functionality of the crosslinks, respectively; N A, k, and T are the Avogadro number, the Boltzmann constant, and the absolute temperature, respectively; and A is a microstructure factor that depends on the ratio between the fluctuation range of a crosslink, d c, and the end to end distance, R c, of a network chain. A is defined as 10 with A K exp K2 erf K (6) K 3 2 1/2 d c (7) R c The parameter allows the connection of the modulus G n with the plateau modulus G o N of the uncrosslinked bulk polymer. The relationship was proposed 9,12 as 3.04 G o 1/2 N G n (8) By using eqs. (4), (5), and (6) it is easy to obtain n st 1.56 G n l st 3 1/ G o N kt 3 l st 1/2 (9) and the fluctuation range of the chain segment d o as 1/2 d o ktl 1/4 st G n (10) The end to end distance of a network chain, R c,is expressed by R c l st M 1/2 ct M st (11)

3 MOLECULAR PARAMETERS OF NR DURING VULCANIZATION. II 2749 Table I Ingredient We can introduce the network chain molecular mass, M ct, as the molecular mass between two crosslinks connected by a polymer chain defined as 13 M ct 1 s M co 1 2M co M n (12) where M co N A /v c, s is the sol fraction of the sample, and v c is obtained as a result of eq. (3). On the other hand, the molecular weight of the network chain between chemical crosslinks for a phantom network, M cs, is expressed by 6,8 M cs 1 2/ V 1v 2/3 1/3 2C v 2m 2 (13) ln 1 v 2m v 2m v 2m where is the density of the network chain, v 2m is the volume fraction of the polymer at the equilibrium (maximum) degree of swelling, V 1 is the molar volume of the solvent; the parameter v 2C is defined by the ratio v d /v o where v d is the volume of the dry network and v o represents the total volume of the polymer; and is an interaction parameter between the polymer and the swelling agent. 8 EXPERIMENTAL Compound Formulation 3 (phr) 1.5 a (phr) SMR Zinc oxide Stearic acid Antioxidant TBBS Sulfur a The formulation used by Mazocca et al. 11 is also shown. Preparation and Characterization of Materials The material used in the present study was an unfilled NR gum mix with the formulation given in Table I. In this table the formulation used in a previous paper is also shown. 11 The number average molecular weight of the elastomer was g/mol as determined by gel permeation chromatography with a density ( ) of g/ml. This polymer corresponds to the same raw material used in a previous study. 11 The gum mix was prepared in a laboratory mill, and after this it was characterized at 414 and 433 K by means of the torque curves in a Monsanto MDR2000 rheometer. From these curves the time to achieve certain degrees of cure, t, was obtained by considering the following relationship that represents the cure degree 14 ( ): o max o 100 (14) where max and o are maximum and minimum torque, respectively, and is the torque at the t time. Various samples were cured at different t at 414 (sample C) and 433 K (sample D). Vulcanized samples were supplied as mm sheets. These specimens were cooled rapidly in ice and water at the end of the curing cycle. In Table II the cure conditions (time and temperature) and the sol fraction ( s ) of each sample are given. The dynamic plateau modulus G N o MPa was measured using an automated torsion pendulum at room temperature and 60 Torr in an argon atmosphere. To evaluate the heat of reaction of each sample produced during vulcanization, differential scanning calorimetry tests were performed with a Mettler TA10 with a DSC20 cell. Samples (15 25 mg) were encapsulated in aluminum holders under nitrogen and scanned at 10 K/min from 303 to 573 K. The overall heat of reaction, Q o, and the heat of reaction up to time t, Q(t), were measured on cured and uncured samples. Then the conversion at time t, (t) (Q o Q(t))/Q o, was calculated and their values are given in Table II. Table II Sample Cure Conditions of Samples Temp. of Cure (K) Cure Time (min) s C C C C D D D D

4 2750 CERVENY AND MARZOCCA Figure 1 Stress strain data and fit curves according to eq. (1) for samples cured at 414 K at different times. Stress Strain Measurements ASTM D412 samples for tensile tests were cut from the cured sheets. Stress strain curves were measured with an Instron 4201 at room temperature at a deformation rate of s 1.A load cell of 50 N was used to obtain good sensitivity. Strain was measured by means of a large deformation extensometer (Instron XL) with a 20-mm gauge length. A PC controlled the tests with software made in Basic language. The stress strain curves were obtained for the three different samples of a given sheet and the average curve was calculated. The standard deviation in the stress of the three tests was less than MPa and for the strain it was insignificant. Swelling Tests The swelling of a rubber compound is frequently used for the determination of the crosslink density. The density of chemical crosslinks was determined using the method described by Cunneen and Russell. 15 The experiment consists of completely immersing a sample in solvent and waiting until swelling equilibrium occurs. The total weight was determined as g for all the samples, then the total number of crosslinks was determined after weighing the samples. The solvent used was n-decane ( dec 0.73 g/mol). 1 and 2, respectively. These figures show the experimental data and the fit curves according to eq. (1), considering 1. The network parameters G c and G n were obtained by the fit of the experimental data, and the values obtained are given in Table III. The error in the determination of G n and G c was less than MPa. The value of G n remained approximately constant for all the samples. Mean values of and MPa were found for samples C and D, respectively. Using eq. (8) with G o N and G n, the values of were estimated for the different samples and they are given in Table III. Information about the network structure can be extracted by means of G c and G n. The n st and d o follow from G n according to eqs. (9) and (10), respectively. Because n st depends on the Kuhn s statistical segment length, l st, it was extracted from the literature. 16 For NR the l st 0.88 nm, then n st 4.06 nm 3 and mean values of d o of 2.61 and 2.54 nm were found for samples C and D, respectively. Considering the molecular mass of the statistical segment as M st N A /n st, a value of g/mol was obtained. The molecular parameters relative to the crosslinks (M ct and v c ) were estimated using the values of G c. From eq. (3) and considering the case of a four functional network, it is possible to calculate the value of the network chain density, v c, and, according to eq. (12), the value of the network chain molecular mass, M ct. Because in these equations the microstructure factor A is involved, then M ct, v c, and A must be iteratively determined using eqs. (6) and (7). The procedure to calculate v c is the following: RESULTS AND DISCUSSION Determination of Network Parameters by Stress Strain Measurements A plot of for the NR gum mix at different times of cure at 414 and 433 K is given in Figures Figure 2 Stress strain data and fit curves according to eq. (1) for samples cured at 433 K at different times.

5 MOLECULAR PARAMETERS OF NR DURING VULCANIZATION. II 2751 Table III Variation of Molecular Parameters of Tube Model with Degree of Cure Sample t (min) G c (MPa) G n (MPa) d o (nm) M co (g/mol) v c (nm 3 ) R c (nm) A C C C C D D D D t, Cure time. 1. Assuming the v c value first, calculate M ct using N A /v c. 2. Solve eq. (12) and calculate R c from eq. (11). 3. Calculate the A value using eqs. (6) and (7). 4. Obtain a new v c value with the A value and eq. (3). 5. With the new v c one can iteratively recalculate up to the converged value. Note that in eq. (7) d o is used instead of d c. This implies that the additional constraints acting on a crosslink are approximately equal to constraints acting on a chain segment. 10 The end to end distance of a network chain, R c, is presented in Table III for both samples according to eq. (11). From the results of R c it can be observed that l st d o R c for each cure level analyzed. This kind of behavior was reported by different authors 9,11 13 in their studies of several elastomers. Effects of Increase of Sulfur/Accelerator Ratio Walter and Helt 4 pointed out that the formation of unstable crosslinks during curing can be controlled by the use of more efficient curing systems. To obtain a more stable crosslink density, the curative levels must be increased by following three basic methods: increase the sulfur, increase the accelerator, or increase both. Compared with previous research in our group 11 when a similar NR compound with a ratio of 1.5 was used, in this work we decreased the level of accelerator while maintaining a constant sulfur level in order to obtain 3. To analyze the performance of the two compounds in the stress strain behavior, the parameters obtained using the tube approach are discussed below. From the values of G n in Table III it is evident that the level of constraints in the material does not depend on the cure level (time and temperature) and the system cure. Obviously, the parameters associated with the constraints, n st and M st, remain as constants in both cases. If we compare the stress strain curves (Figs. 1, 2) we observe that in the overcure samples a high reversion effect in the tensile properties takes place. This behavior can be attributed to some effect associated with the nature and density of the crosslinks. These findings agree with those previously reported. 11 Figures 3 and 4 show the variation in G c with the degree of cure for both ratios of sulfur/accelerator at 414 and 433 K, respectively. The results Figure 3 The effect of the time of cure and the ratio of the sulfur/accelerator ( ) on the modulus contribution of the crosslink, G c, at 414 K.

6 2752 CERVENY AND MARZOCCA Figure 4 The effect of the time of cure and the ratio of the sulfur/accelerator ( ) on the modulus contribution of the crosslink, G c, at 433 K. show that the cure affects the values obtained for all samples and the increase in the concentration of accelerator in the compound implies high values of G c. The growth in the cure temperature amplifies the difference between the values of G c at different levels, which can be deduced by comparing Figures 3 and 4. The crosslink density is also modified by the ratio of the sulfur/accelerator as shown in Figures 5 and 6 where the v c decreases when the ratio of the sulfur/accelerator increases. It is interesting to note that as the cure temperature increases, although the amount of sulfur remains constant, the efficiency of vulcanization falls and this effect is larger when the time of cure is longer. Walker and Helt 4 reported similar results in NR cured at 414 and 453 K but with another accelerator N- cyclohexylbenzothiazole-2-sulphenamide (CBS). In that research they found that essentially monosulfidic crosslinks were obtained. We are interested in analyzing the evolution of the network chain density following the contribution of crosslink formation and degradation. If we consider that there are no chemical crosslinks at the onset of the cure reaction, v c could be fit as a function of the cure time t using the model in which crosslinking and degradation are assumed to be a first-order reaction, 17,18 v c C exp[ 1 t t o exp[ 2 t t o ]} (15) where 1 and 2 are associated with the rate constants of crosslinking and degradation, respectively, and t o is an induction time. It is clear from Figures 5 and 6 that the model provides a good fit to the data of v c for both cure temperatures and values. These plots also give the adjustments of v c obtained for the present data given in a previous study 11 for a similar NR gum with 1.5. Figure 5 A comparison between the calculated crosslink densities v c and the fit curves using eq. (15) and (inset) v c / t for samples vulcanized at 431 K at two s.

7 MOLECULAR PARAMETERS OF NR DURING VULCANIZATION. II 2753 Figure 6 A comparison between the calculated crosslink densities v c and the fit curves using eq. (15) and (inset) v c / t for samples vulcanized at 433 K at two s. The parameters C, 1, and 2 are reported in Table IV for each level of cure temperature and sulfur/accelerator ratio. The insets in Figures 5 and 6 illustrate the v c / t corresponding to each analyzed case. Note from Table IV that the rate of crosslinking increases with the temperature of cure and at higher values of. It is apparent for v c / t that the rate of degradation, once the maximum of v c is attained, is higher in the case of 3 at 414 and 433 K. Our recipes are in accord with the conventional vulcanization (CV) system in which more polysulfidic crosslinks and more sulfur combined with rubber chains to form sulfur rings along the rubber molecular chain are present. 19 When increasing the concentration of the accelerator in the recipe, going from a CV system to an efficient vulcanization (semi EV or EV), the desulfuration of polysulfide crosslinks is very rapid and there is little crosslink elimination or main chain modification. 3 In this last case the crosslinks are shorter than those formed in compounds with the CV system and this should give the best retention of crosslink density as cure temperature increases, forming a more stable network structure. Although in this work we are comparing two NR gum mixes with two cure systems in the CV region, we observed that the recipe with higher accelerator concentration ( 1.5) gives a more stable structure for the overcure samples at both cure temperatures analyzed. Determination of Chemical Crosslink Density by Swelling Test The density of the chemical crosslinks was estimated from swelling for all samples. The values Table IV Variation of Parameters of Eq. (15) with Temperature of Cure and C (nm 3 ) 1 (min 1 ) 2 (min 1 ) 414 K 433 K 414 K 433 K 414 K 433 K

8 2754 CERVENY AND MARZOCCA Table V Molecular Weight of Network Chain Obtained by Analysis of Stress Strain Data (M ct ) and Swelling Measurement (M cs ) those calculated from the stress strain data in the frame of the configurational tube model. Sample Cure Time (min) M ct (g/mol) M cs (g/mol) CONCLUSIONS C C C C D D D D obtained for M cs using eq. (13) are given in Table V. For these estimations a value of 0.43 for NR was used 15 and v 2C was considered to be equal to 1. With the goal of comparing the results obtained for the mechanical and swelling methods, the density of elastically active crosslink, c, was calculated. In a four functional network assumed in the present case, c is related to the density of all the network chains, v o,by 20 v o 2 c v n (16) where v n is the density of the primary chain prior to vulcanization. The v o and v n can both be transformed to molecular weights by v o /M C and v n /M n. Then c is defined by This work presents the changes in the network parameters of NR vulcanizates at two sulfur/accelerator ratios,. Relevant parameters (the network chain molecular mass and the network chain density) were evaluated using the tube model that takes into account the restrictions of conformation of polymer network chains. This model was applied to uniaxial stress strain data at different cure conditions. Our results show that if the ratio of the sulfur/accelerator is decreased in the compound formulation by a change in the accelerator concentration, the network chain density will increase at both curing temperatures analyzed. We verified that there is a dependence of the rate of crosslinking ( 1 ) and degradation ( 2 )on. In fact, 1 is higher at higher levels of. Moreover, the compound with lower presents a more stable structure under overcure. We also compared the results of the chemical crosslinks obtained by means of the mechanical analysis with that of the swelling measurements. There was a good correspondence in this value at 414 K. However, the test performed at 433 K showed a small difference with higher values of obtained in the mechanical analysis. c 2 1 M C 1 M n (17) where M C is the network chain molecular mass. If we replace M C by M ct in eq. (17), we obtain the density of elastically active crosslinks calculated from the stress strain measurements, ct. On the other hand, if we use the value of M cs, we obtain the density of elastically active crosslinks calculated from swelling measurements, cs. In Figure 7 ct is plotted against cs. In this figure the values obtained from samples of NR gum mixes with and those calculated in this work were included. The data can be fit by a linear regression with a slope of and a regression coefficient (R 2 ) of This fact points out that there is a good correspondence between the values obtained by swelling and Figure 7 The density of elastically active crosslinks obtained from the analysis of stress strain data ct versus those calculated from swelling measurements cs for 1.5 and 3.

9 MOLECULAR PARAMETERS OF NR DURING VULCANIZATION. II 2755 The second author wishes to thank FATE SAICI for the sample preparation. REFERENCES 1. Chough, S.; Chang, D. J Appl Polym Sci 1996, 61, Loo, T. Polymer 1974, 15, Doyle, G. M.; Humphereys, R. E.; Russell, R. M. Rubber Chem Technol 1972, 15, Walker, L. A.; Helt, W. F. Rubber Chem Technol 1986, 59, Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953; p Queslel, J. P.; Mark, J. E. J Chem Phys 1985, 82, Queslel, J. P.; Mark, J. E. Adv Polym Sci 1985, 71, Mark, J. E.; Erman, B. Rubberlike Elasticity: A Molecular Primer; Wiley: New York, 1988; p Heinrich, G.; Straube, E.; Helmis, G. Adv Polym Sci 1988, 85, Straube, E.; Heinrich, G. Kautsch Gummi Kunst 1991, 44, Marzocca, A. J.; Cerveny, S.; Raimondo, R. B. J Appl Polym Sci 1997, 66, Heinrich, G.; Vilgis, T. A. Macromolecules 1993, 26, Marzocca, J. A. J Appl Polym Sci 1995, 58, Hill, D. A. Heat Transfer & Vulcanization of Rubbers; Elsevier: London, 1971; p Cunneen, J. I.; Russell R. M., Rubber Chem Technol 1970, 43, Aharoni, S. Macromolecules 1986, 19, Scheele, W. Rubber Chem Technol 1961, 34, Jurkowski, B.; Kubis, J. Kautsch Gummi Kunst 1985, 38, Coran, A. Y. In Science and Technology of Rubber, 2nd ed.; Mark, J. E.; Erman, B.; Eirich, F. R., Eds.; Academic: San Diego, CA, 1994; p Gronski, W.; Hoffmann, V.; Simon, G.; Wutzler, A.; Straube, E. Rubber Chem Technol 1991, 65, 63.